Extended Data Fig. 7: Lagged cross-covariance and coherence between calcium and total hemoglobin recapitulate DOI-induced changes in neurovascular coupling.

a) Global hemodynamic response functions: The global HRF estimated using deconvolution following DOI injection (4mg/kg, \(n=8\), top; Fig. 4a) and the global lagged cross-covariance function (CCF; bottom) between resting-state calcium and hemodynamics. Pre-injection CCFs display a simple, quasi-causal relation (calcium leads hemodynamics). DOI decreased coupling (peak value, -51% [-66%, -13%], pre- vs. post-injection: p=0.039; Kruskal-Wallis: p=0.004; saline vs. DOI: p=0.020; DOI vs. DOI+MDL: p=0.004; DOI vs. MDL (0.1mg/kg): p<0.001). DOI induced a zero-lag notch in the CCF (black arrow). Covariance has units of \(\Delta \mu\)Mol\(\Delta\)F/F(%) and the HRF has units of \(\Delta \mu\)Mol/\(\Delta\)F/F(%). b) DOI-induced alterations in CCF over the cortex. Regional distribution of cross covariance after the injection of DOI reveals a negative-lag peak across the cortex. CCFs for all regions and compounds are displayed in Supplementary Fig. S6a. c) Magnitude Squared Coherence (MSC) between calcium and hemodynamic activity. Before compound injection, MSC exhibited a large 0.2Hz peak, demonstrating the band-limited nature of NVC. After injection of DOI, a coherence peak ~0.8Hz (~0.5Hz half-bandwidth) emerged (0.5-2.0Hz: +170% [110% 230%]; pre- vs. post-injection: p=0.008; Kruskal-Wallis: p=0.004; saline vs. DOI: p=0.009; DOI vs. DOI+MDL: p=0.030; DOI vs. MDL: p=0.025). Moreover, the 0.2Hz peak present before injection largely diminished (<0.5Hz: -47% [-53%, 49%], pre- vs. post-injection: p=0.008). This phenomenon signifies a DOI-induced shift in the coherent frequencies contained in both neuronal and hemodynamic activity. DOI+MDL largely reversed the effects of DOI alone (Supplementary Fig. S6). Coherence for all regions and compounds are displayed in Supplementary Fig. S6b. d) Phase relation between calcium and hemodynamics. Prior to injection, global calcium activity led hemodynamic activity (positive slope at frequencies below ~1Hz; left). After DOI injection, phase relations between calcium and hemodynamic activity flipped sign (for example, from positive to negative slope in primary motor and primary somatosensory hindpaw; right), indicating that hemodynamics precede calcium over these frequencies. Supplementary Fig. S6c reports phase relations for all regions and compounds. All data are presented mean ± std across mice. Significance was determined via Kruskal-Wallis tests and post-hoc, two-sided Wilcoxon’s sign-rank corrected post-hoc using Bonferroni correction.